Refraction of Light by Rectangular Prism

When a ray of light enters a prism, it bends towards the normal (since glass is denser than air). Upon leaving, it bends away from the normal. This overall change in direction is called the angle of deviation (D).

• Angle of deviation (D): The angle between the direction of the incident ray and the emergent ray.

Behavior of deviation:

1. As the angle of incidence increases, deviation decreases to a minimum value (d), then increases again.
2. This minimum deviation is important in determining the refractive index of the prism.

Formula for refractive index using minimum deviation:

$n = \frac{\sin\left(\frac{A + d}{2}\right)}{\sin\left(\frac{A}{2}\right)}$

Where:

n = refractive index

A = angle of prism

d = minimum deviation

Dispersion is the splitting of white light into its seven component colors when it passes through a prism.

• These seven colors form a spectrum: Red, Orange, Yellow, Green, Blue, Indigo, Violet (ROYGBIV).

• A pure spectrum has distinct, non-overlapping colors.

  

• An impure spectrum has overlapping or unclear boundaries between the colors.

Why dispersion happens:

• Each color of light bends (refracts) at a different angle due to its different wavelength.

Combining spectrum colors:

• Using a second prism and a lens, we can recombine the spectrum into white light again.

A rainbow is a natural example of dispersion.

How it forms:

• Light enters raindrops in the atmosphere.
• It refracts, undergoes internal reflection, and refracts again as it exits.
• The different colors bend at different angles forming a circular spectrum.

Types of rainbows:

1. Primary rainbow:

   • Formed by one internal reflection.

   • Red is on the outside; violet is on the inside.

     

2. Secondary rainbow:

   • Formed by two internal reflections.
   • Fainter and has colors in reverse order.

Important terms recap:

Term	Meaning
Angle of Incidence (i)	Angle between incident ray and the normal
Angle of Refraction (r)	Angle between refracted ray and the normal
Refractive Index (n)	How much a ray bends in a medium
Deviation (D)	Bending of the entire ray path in a prism
Minimum Deviation (d)	The least amount by which light is bent by a prism
Spectrum	The band of colors produced by dispersion
Pure Spectrum	Clear, non-overlapping band of colors
Impure Spectrum	Overlapping or unclear colors in the band

Example:

Calculate the refractive index of a glass prism if the angle of prism is 60º and the minimum deviation is 40º.

Solution:

Given:

• A = 60º
• d = 40º

Using the formula:

$n = \frac{\sin\left(\frac{A + d}{2}\right)}{\sin\left(\frac{A}{2}\right)} = \frac{\sin\left(\frac{60 + 40}{2}\right)}{\sin\left(\frac{60}{2}\right)} = \frac{\sin(50º)}{\sin(30º)} = \frac{0.7660}{0.5} = 1.532$

Answer: Refractive index, n = 1.532

Simple prism binocular